Democracy & Nature, Vol. 6, No. 3, 2000 Systems Theory and Complexity Introduction ARRAN GARE ABSTRACT In this paper the central ideas and history of complexity theory and systems theory are described. It is shown how these theories lend themselves to different interpretations, and different interpretations lead to different political conclusions. 1. Introduction At the turn of the millennium, the study of complex systems has become one of the most prominent elds of scienti c study. This is, according to those engaged in it, a revolution of major proportions. ‘Science has explored the microcosmos and the macrocosmos’, wrote Heinz Pagels in The Dreams of Reason, ‘The great unexplored frontier is complexity’.1 But according to some of the more radical complexity theorists, there is more to complexity than an unexplored domain. While previously science had struggled to reveal the simple behind the complex, it is now being suggested by some theorists that the world is irreducibly complex. The task before us is no longer to identify the simple elements of reality underlying complex appearances but to work out how to study complexity in its own right. A whole range of phenomena, previously disregarded by mainstream science, has become the central focus of some of the world’s most eminent scientists. Instead of being taken as the foundation of science, simplicity is now coming to be regarded by some theorists as one of the products of complexity.2 Almost every discipline from physics and chemistry to neurobiol- ogy, economics, politics and history has been forced to confront the issues raised by complexity theorists and to explore the relevance of their ideas. And not only have the boundaries between scienti c disciplines been crossed, including the boundaries between the natural and the human sciences; the boundaries between science, the humanities and the arts have also have been brought into question. As Brian Goodwin claimed at a conference at the Santa Fe Institute, ‘complexity is moving towards … a nondisciplinary, integrated science which actually goes beyond science. It goes right into the so-called social sciences, and now I think 1. Cited by Roger Lewin, Complexity: Life on the Edge of Chaos (London: Phoenix, 1993), p. 10. 2. This is the thesis of Jack Cohen and Ian Stewart, The Collapse of Chaos: Discovering Simplicity in a Complex World (Harmondsworth: Penguin, 1994). 3. George A. Cowan, David Pines and David Meltzer, eds, Complexity: Metaphors, Models and Reality, Proceedings, Vol. XIX, Santa Fe Institute Studies in the Sciences of Complexity (Reading, MA: Addison-Wesley, 1994), p. 672. ISSN 1085-5661 print; 1469-3720 online/00/03/0327-13 Ó 2000 Democracy & Nature 327 DOI: 10.1080/10855660020020221 Arran Gare that it goes into the arts as well.’3 The focus on complexity has revived interest in schools of thought and the work of philosophers and scientists who have in the past struggled to develop alternatives to reductionist science. Prominent among these are general systems theorists, process philosophers and dialectical naturalists. What is the science of complex systems? What is its relation to earlier movements of thought? And what is the relevance of all these ideas to the project of developing an inclusive democracy? This is the topic of this special edition of Democracy and Nature. Here I will give a brief overview of complexity theory and systems theory and the issues raised by their work. 2. The project of the Santa Fe Institute Complexity theory came to public prominence with the establishment in 1984 of the Santa Fe Institute; and since then, the study of complexity has been almost identi ed with research at the Institute.4 With the participation of several Nobel Laureates (Murray Gell-Mann, Kenneth Arrow and Philip Anderson) and other scienti c celebrities along with a number of ambitious younger scientists, members of the Institute set out to create a new synthesis involving mathematics, computational science, physics, chemistry, biology, neuroscience and the social sciences. Focussing on the behaviour and evolution of ‘complex, adaptive systems’, researchers at the Institute set out to reintegrate the fragmented interests in complex phenomena of much of the academic community. ‘Com- plexity’ was taken to refer to, in the words of the Founding President of the Institute, George Cowan, ‘systems with many different parts which, by a rather mysterious process of self-organization, become more ordered and more in- formed than systems which operate in approximate thermodynamic equilibrium with their surroundings’.5 ‘The central goal of the sciences of complex systems,’ wrote Mitchell, Cruch eld and Hraber, ‘is to understand the laws and mecha- nisms by which complicated, coherent global behaviour can emerge from the collective activities of relatively simple, locally interacting components. ’6 The ight of a ock of birds ying in formation or schools of sh swimming in a coherent array suddenly changing direction although there is no leader guiding the group, are simple examples of such emergence. And much the same crowd behaviour is identi able in the buying and selling of stocks in the stock market. In complex adaptive systems, interacting components generate an emergent global order that is able to adapt to new circumstances and, in doing so, to act 4. For an entertaining account of the Santa Fe Institute, see M. Mitchell Waldrop, Complexity: The Emerging Science at the Edge of Order and Chaos (New York: Touchstone, 1992). The Santa Fe Institute have published an enormous number of proceedings on a wide range of topics, but the volumes that gives the best overview of their work are David Pines, ed., Emerging Syntheses in Science, Proceedings, Vol. I, Santa Fe Institute Studies in the Sciences of Complexity (Reading, MA: Addison-Wesley, 1987), and Cowan et al., Complexity: Metaphors, Models and Reality. 5. George A. Cowan, ‘Conference Opening Remarks’, in Cowan et al., Complexity: Metaphors, Models and Reality, p. 1. 6. Melanie Mitchell, James P. Crutch eld and Peter T. Hraber, ‘Dynamics, Computation, and the “Edge of Chaos”: A Re-Examination’, in Cowan et al., Complexity: Metaphors, Models and Reality, p. 498. 328 Systems Theory and Complexity back on the components. The operation of complex adaptive systems, according to Gell-Mann, ‘encompasses such diverse processes as the prebiotic chemical reactions that produced life on Earth, biological evolution itself, the functioning of individual organisms and individual communities, the operation of biological subsystems such as mammalian immune systems or human brains, aspects of human cultural evolution, and adaptive functioning of computer hardware and software’.7 The programme of the Santa Fe Institute was de ned by Cowan at one of the Institute ’s conferences: The program deals with the appearance of folded proteins and the beginning of highly interconnected, self-organizing, and adaptive sys- tems. It ranges from the formation of cells and organs, particularly including the brain, to organism, particularly man, and the enormously interactive systems studied in social science. The human dimension really begins with nature’s invention of the human cortex, a prerequi- site for the invention of symbols, language, culture, electronic com- munication, and the evolving behavior of collective units which have increased in size until they now embrace a truly global community.8 Members of the Institute have made advances in most of these elds. Their achievements have inspired work in a host of disciplines beyond those considered by members of the Institute, including management studies. Cowan has acknowledged von Bertalanffy’s general systems theory, White- head’s philosophy of organism, McCulloch and Pitts on neural networks, von Neumann on cellular automata and complexity, Wiener on cybernetics, Pri- gogine on dissipative structures associated with non-linear thermodynamics and Haken’s synergetics as precursors to the Santa Fe’s study of complexity. He attributes renewed interest in complexity to the greater accessibility of comput- ers. Many of the Institute’s members have been concerned to exploit the potential of computers to examine mathematical relationships previously too dif cult to study and for their powers to simulate natural processes. In doing so, members of the group have drawn on the mathematics of dynamical systems (including chaos theory, catastrophe theory and bifurcation theory) characterised by point, limit cycle and strange attractors. They have also embraced fractals, information theory, arti cial intelligence, computational theory, cellular au- tomata, Boolean networks, neural nets and genetic algorithms (which mimic a Darwinian selection process to arrive at solutions to problems). Dynamical systems theory and cellular automata have been particularly signi cant. 3. Central ideas and approaches of the Santa Fe Institute Dynamical systems are not systems in the world but mathematical models of systems. The advantage of dynamical systems as a form of representation is that it makes possible use non-linear equations, equations in which dependent variables (y in the equation y 5 f(x)) must appear in higher powers than one. 7. Murray Gell-Mann, ‘Complex Adaptive Systems’, p. 18. 8. Cowan, ‘Conference Opening Remarks’, p. 2f. 329 Arran Gare Computers have enabled us to deal with such equations that previously, because they were insoluble, were ignored. What this means is that with dynamical systems using non-linear equations there are no longer simple ratios between causes and effects; in the long run a small cause can have a major effect. This notion has been popularised as the butter y effect—a butter y apping its wings in USA could cause a hurricane in China. A system can be any collection of objects or processes deemed to be of interest. Dynamical systems have two parts: a representation of all possible states of the system, called the manifold of the system (often represented using phase space), and a set of equations that describes how the state of the system changes with time.